Vol. 304, No. 2, 2020

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Regularity of quotients of Drinfeld modular schemes

Satoshi Kondo and Seidai Yasuda

Vol. 304 (2020), No. 2, 481–503
Abstract

Let A be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal I A, Drinfeld defined the notion of structure of level I on a Drinfeld module.

We extend this to that of level N, where N is a finitely generated torsion A-module. The case where N = (I1A)d, where d is the rank of the Drinfeld module, coincides with the structure of level I. The moduli functor is representable by a regular affine scheme.

The automorphism group AutA(N) acts on the moduli space. Our theorem gives a class of subgroups for which the quotient of the moduli scheme is regular. Examples include generalizations of Γ0 and of Γ1. We also show that parabolic subgroups appearing in the definition of Hecke correspondences are such subgroups.

Keywords
Drinfeld modular schemes, Drinfeld level structures, regularity
Mathematical Subject Classification 2010
Primary: 11F32
Secondary: 14G35
Milestones
Received: 21 August 2017
Revised: 10 August 2019
Accepted: 11 August 2019
Published: 12 February 2020
Authors
Satoshi Kondo
METU Northern Cyprus Campus
Kalkanlı
Güzelyurt
Mersin 10
Cyprus
Seidai Yasuda
Osaka University
Toyonaka
Osaka
Japan